Quantum Resonance Interferometry for Detecting Signals

ABSTRACT

A computer-implemented method for signal analysis includes receiving a first signal, receiving a second signal, coupling the first signal with a first function generated from a first quantum mechanical system to generate a first tunneling rate, coupling the second signal with a second function generated from a second quantum mechanical system to generate a second tunneling rate, coupling the first tunneling rate with a third function generated from a third quantum mechanical system, coupling the second tunneling rate with the third function, obtaining a third tunneling rate, and upon determining that the third tunneling rate is greater than a threshold, identifying that the second signal corresponds to the first signal.

CROSS REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of the priority of U.S. ApplicationSer. No. 11/835,378 filed on Aug. 7, 2007, which claims the benefit ofpriority of U.S. Provisional Application Ser. No. 60/836,211 filed onAug. 7, 2006, and entitled “QRI PREAMPLIFIER FOR ENHANCING GPS RECEIVERPERFORMANCE.” The entire contents of both applications are incorporatedherein by reference.

INCORPORATION BY REFERENCE OF A COMPUTER PROGRAM LISTING

An electronic version of the computer program listing, created on Aug.7, 2007, is filed herewith, the contents of which are incorporated byreference in their entirety.

TECHNICAL FIELD

This disclosure relates to signal detection and noise reduction usingtechniques, e.g., quantum resonance interferometry.

BACKGROUND

Experimentally acquired data typically includes noise in addition tosignals representing information and/or events of interest. The noiserepresents undesired variations that are not related to the desireddata. For example, the acquired data can include stochastic variationsgenerated by interactions with the environment surrounding a measuredsystem or a detector acquiring the data. Noise can be generated withinthe measured system by events that are unrelated to the information ofinterest. Noise may also be generated when the acquired data istransmitted or processed, for example, when it is digitized. Noise canbe a significant problem with devices employing an array of sensors inwhich there are numerous sources of signals.

Interferometry can measure very small differences in lengths, distancesand changes in dimension density and other properties by theinterference of two waves of light for optical imaging and communicationapplications. Quantum Resonance Interferometry (QRI) deliverssignal-to-noise enhancement by interference between a wave equationrepresentation of both the sensor-specific noise model and unknownincoming data containing a potential target or event of interest. Withinthe QRI formalism, signal can represent a specific target signature ofinterest, and all other target nonspecific background (including sensor)noise and clutter can be noise. QRI hypothesizes signal as a disturbanceto noise, and re-formulates target detection/discrimination problems tobe developing a compact a noise model for sensor physics.

SUMMARY

In one embodiment, a first signal and a second signal, both buried innoise, are received where the first signal can be a reference signal andthe second signal can be signal obtained from an unknown source. A noisemodel, representing the first signal, can be generated andinterferometrically coupled with an expresser function to detect quantumstochastic resonance (QSR). The QSR determination can identify a firsttunneling rate corresponding to the first signal. Similarly, a noisemodel, representing the second signal, can be generated andinterferometrically coupled with an expresser function to detect QSR,and a second tunneling rate corresponding to the second signal can bedetermined. Subsequently, the first tunneling rate and the secondtunneling rate can be interferometrically coupled with an expresserfunction to enable determining if the second signal corresponds to thefirst signal. The interferometric coupling of the first and secondtunneling rates with an expresser function can produce a third tunnelingrate which can indicate that the second signal corresponds to the firstsignal if the third tunneling rate is greater than a threshold. Forexample, if the third tunneling rate is greater than the threshold, thenthe unknown signal can be substantially identical to the referencesignal, thereby enabling identifying the source of the second signal.

In one aspect, a computer-implemented method for signal analysis isdescribed. The method includes receiving a first signal, receiving asecond signal, coupling the first signal with a first function generatedfrom a first quantum mechanical system to generate a first tunnelingrate, coupling the second signal with a second function generated from asecond quantum mechanical system to generate a second tunneling rate,coupling the first tunneling rate with a third function generated from athird quantum mechanical system, coupling the second tunneling rate withthe third function, obtaining a third tunneling rate, and upondetermining that the third tunneling rate is greater than a threshold,identifying that the second signal corresponds to the first signal.

This, and other aspects, can include one or more of the followingfeatures. The first signal can be a reference signal and the secondsignal can be an unknown signal. The second signal can be substantiallysimilar to the first signal if the second signal corresponds to thefirst signal. Coupling the first signal with a first function caninclude initializing a first dynamical system corresponding to a firstmodality of the first signal, generating a first measurement probe basedon the initialized first dynamical system, injecting the firstmeasurement probe into the first quantum mechanical system, anddetermining whether the injection of the first measurement probe intothe first quantum mechanical system results in a collapse of the firstquantum mechanical system. A collapse of the first quantum mechanicalsystem can indicate resonance between the first measurement probe andthe first quantum mechanical system. The first tunneling rate and thesecond tunneling rate can be pre-conditioned prior to coupling with thethird function. Pre-conditioning the first tunneling rate and the secondtunneling rate can include converting the first tunneling rate and thesecond tunneling rate into respective spectral domains.

In another aspect, a computer-implemented method for signal analysis isdescribed. The method includes receiving an unknown signal, coupling theunknown signal with a function generated from a quantum mechanicalsystem to generate a tunneling rate associated with the unknown signal,pre-conditioning the tunneling rate, coupling the pre-conditionedtunneling rate with a reference tunneling rate obtained from a referencesignal to generate an output tunneling rate, and upon determining thatthe output tunneling rate is greater than a threshold, determining thatthe unknown signal corresponds to the reference signal.

This, and other aspects, can include one or more of the followingfeatures. The unknown signal can include one of the reference signal,noise, or a non-specific signal. Coupling the unknown signal with thefunction can include initializing a dynamical system corresponding to amodality of the unknown signal, generating a measurement probe based onthe initialized dynamical system, injecting the measurement probe intothe quantum mechanical system, and determining whether the injection ofthe measurement probe into the quantum mechanical system results in acollapse of the quantum mechanical system. A collapse of the quantummechanical system can indicate resonance between the measurement probeand the quantum mechanical system. The method can further includepre-conditioning the tunneling rate by applying a Fast FourierTransform. The reference tunneling rate can be pre-conditioned prior tocoupling with the pre-conditioned tunneling rate. The reference signalcan be obtained from a known source. Determining that the unknown signalcorresponds to the reference signal can include determining that theunknown signal is substantially similar to the reference signal.

In another aspect, a system for signal analysis is described. The systemincludes a function generator to generate a first function, a secondfunction, and a third function from one or more quantum mechanicalsystems, a first interferometric coupler to couple a first signal withthe first function to generate a first tunneling rate, a secondinterferometric coupler to couple a second signal with the secondfunction to generate a second tunneling rate, a first pre-conditioner topre-condition the first tunneling rate, a second pre-conditioner topre-condition the second tunneling rate, a third interferometric couplerto couple the pre-conditioned first tunneling rate with the thirdfunction and to couple the pre-conditioned second tunneling rate withthe third function, the third interferometric coupler configured togenerate a third tunneling rate, and a comparator to compare the thirdtunneling rate with a threshold to determine if the third tunneling rateis greater than, or less than or equal to the threshold.

This, and other aspects, can include one or more of the followingfeatures. The first signal can be a reference signal and the secondsignal can be an unknown signal. The second signal can be substantiallysimilar to the first signal if the third tunneling rate is greater thanthe threshold. The first interferometric coupler can be configured toperform operations including initializing a first dynamical systemcorresponding to a first modality of the first signal, generating afirst measurement probe based on the initialized first dynamical system,injecting the first measurement probe into the first quantum mechanicalsystem, and determining whether the injection of the first measurementprobe into the first quantum mechanical system results in a collapse ofthe first quantum mechanical system. A collapse of the first quantummechanical system can indicate resonance between the first measurementprobe and the first quantum mechanical system.

In another aspect, a computer program product, tangibly embodied in acomputer-readable medium is described. The computer program product isconfigured to cause a machine to perform operations. The operationsinclude receiving an unknown signal, coupling the unknown signal with afunction generated from a quantum mechanical system to generate atunneling rate associated with the unknown signal, pre-conditioning thetunneling rate, coupling the pre-conditioned tunneling rate with areference tunneling rate obtained from a reference signal to generate anoutput tunneling rate, and upon determining that the output tunnelingrate is greater than a threshold, determining that the unknown signalcorresponds to the reference signal.

This, and other aspects, can include one or more of the followingfeatures. The unknown signal can include one of the reference signal,noise, or a non-specific signal. Coupling the unknown signal with thefunction can include initializing a dynamical system corresponding to amodality of the unknown signal, generating a measurement probe based onthe initialized dynamical system, generating a measurement probe basedon the initialized dynamical system, injecting the measurement probeinto the quantum mechanical system, and determining whether theinjection of the measurement probe into the quantum mechanical systemresults in a collapse of the quantum mechanical system. A collapse ofthe quantum mechanical system can indicate resonance between themeasurement probe and the quantum mechanical system. The operations canfurther include pre-conditioning the tunneling rate by applying a FastFourier Transform. The reference tunneling rate can be pre-conditionedprior to coupling with the pre-conditioned tunneling rate. The referencesignal can be obtained from a known source. Determining that the unknownsignal corresponds to the reference signal can include determining thatthe unknown signal is substantially similar to the reference signal.

The systems and techniques described here can present one or more of thefollowing advantages. Signals below the noise level can be detected fora large number of different microarray types, including glass based,thin film, electronic, bead or quantum dot arrays. The signal analysisis not limited to particular methods or apparatus that are used toacquire the data. If the reference signal is obtained from a human andthe unknown signal is obtained from two sources, e.g., a tree and ahuman standing next to the tree, the noise reduction technique candetect that the unknown signal includes signal from the human and fromthe tree. Noise can be analyzed in reference samples to define anon-linear dynamical model for signal analysis. The non-linear dynamicalmodel can be defined “off-line,” i.e., before analyzing actual samples.The same non-linear dynamical model can be used for the samepre-characterized platform. With the present techniques, a large numberof samples can be analyzed in a short time.

The details of one or more implementations are set forth in theaccompanying drawings and the description below. Other features andadvantages will be apparent from the description and drawings, and fromthe claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is an example of a schematic of an interferometric system.

FIG. 2 is a flow chart of a process for causing the collapse of aquantum mechanical system.

FIG. 3 is a flow chart of a process for using QRI to determine thepresence of a signal in incoming data.

FIG. 4 is a schematic of a QRI engine for signal analysis.

FIG. 5 is a schematic of an example of a QRI engine.

FIG. 6 is a flow chart of a process for generating QEF to drive activesignal analysis.

FIG. 7 is a schematic of a differential interference protocol.

FIG. 8 is an illustration of using a driving force impulse to excite atwo-state system.

FIG. 9 is a schematic of a diagram for detecting signals using theexpresser function.

FIG. 10 is a schematic of a system for identifying clutter and signal.

FIG. 11 is a flow chart of an example of a process for identifyingclutter and signal.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

In QRI, a compact set of training samples, including exemplars oftargets of interest, representative backgrounds, and operational sensormodalities are used to develop a quantum expresser function (QEF). Thiscan also be referred to as the non-specific target noise model for thesensor. QRI uses a computational engine to implement the interactionbetween the QEF (or probing noise stimulus) and the incominguncharacterized signals of interest. As the acquired data includesnoise, in addition to signals representing information and events ofinterest, QRI addresses multiple sources of noise simultaneously. Forexample, the acquired data can include stochastic variations generatedby interactions with the environment surrounding a measurement system ora detector acquiring the data. Clutter or background noise can begenerated within the measurement system by the events that are unrelatedto the information of interest. For example, noise can be generated whenthe acquired data is digitized or transmitted. QEF represents the “noisemodel” for the system for a pre-specified target performance condition,e.g., detectability down to a given limit of detection (LOD). The QEFfidelity is modality specific, e.g., a collection of pixels on a focalplane, a spectral segment of absolute abundance data for a mass specdetector, and the like. The QEF fidelity can correspond to the minimumamount of signal required within incoming data required to concludesignal presence. The incoming unknown data can initially be assumed tobe all noise. Interferometric computations between QEF and the incomingdata to induce computational resonances can be used to detect signal, asa departure to noise behavior wherein no resonances are observed.

In some implementations of a QRI solution, unknown incoming signals andapriori generated QEF can both be mathematically represented toinitialize a wave equation system. QRI leverages the dynamics andproperties of a well understood 1-D Spin-Boson quantum mechanical systemto develop the wave equation mathematical representation for incomingsensor data and noise model. The two wave equations are destructivelyinterfered to detect the presence of a target buried in noise. Anoptimal and robust QEF can be developed based on the noise and detectioncharacteristics of the sensor physics. Once a QEF has been designed,emulated signals, characteristic of the targets, can be iterativelyinjected into the signal data to be tested. Any fragment of targetsignature present in the incoming data, above the pre-specified limit ofdetection (LOD) can yield a resonance event when interfered with a QEF.QRI employs wave equation dynamics, such as the time evolution equationof a Spin-Boson (S-B) bi-stable system, as the underlying model forclutter detection.

The tunneling or interwell transition rate is a computational observablefor the S-B dynamics simulation. In an S-B dynamics simulation, the bathtemperature is varied to change the tunneling rate. From an algorithmicperspective, noise can be added to the system to simulate bathtemperature changes and to modulate the properties of the system. An S-Bsystem can exhibit quantum stochastic resonance phenomena where thesignal-to-noise ratio (SNR) of the output signal is maximized. WithinQRI, the dependent variable in the governing differential equation,namely the variable out of which the output (processed) signal isextracted, represents quantum amplitudes and probabilities. In someimplementations, a semi-classical approximation is employed, whereby thequantum dynamical equations reduce to coupled ordinary differentialequations for the interwell instantaneous transition rates, as well asother, uniquely quantum dynamical entities called coherences. Thisapproximation can yield a variety of injected noises due to theinterplay of interwell tunneling in a bi-stable S-B system, and thenormalization, which, when optimized, can result in a high SNR gainfactor. The governing equations of the QRI are linear in the dependentvariables, and do not require an explicit injected noise term (additiveor otherwise). The nonlinearity can enter through the way in which theinput signal modulates the dynamics and the injected noise, can enterthrough a relaxation time, or times, stemming from quantum decoherencedue to interactions of the quantum system with its environment, whichthus effects a partial quantum measurement upon the system. Another wayin which noise can be injected can be via a quantum friction, where thequantum friction can be induced by the interaction of the quantum systembut its environment. The complex concepts of noise injection can beexpressed in terms of matrix vector operations using transformations andquantum trajectory approximations, and implemented using digitalprocessors.

FIG. 1 depicts a schematic of a QRI system 100 including a QEF 105interferometrically coupled with incoming pre-conditioned sensor data110 using an interferometric coupler 115 to detect weak signals buriedin noise. The incoming input data can include single or multiplemodality data, e.g., spatial, temporal, spatio-temporal, symbolic,spectral, spatio-spectral, audio, video, RF, and the like. The incominginput data can be derived from one or more detector elements. Theresulting data (enhanced result 120) can be used to identify one or moreevents of interest within the incoming data that might not otherwise beidentified without the interferometric coupling.

QRI solution development can include two stages: a design stage and anoperational stage. The design stage can focus on QEF development for apre-characterized platform, analyzing noise in the acquired data setusing calibrated reference samples, and designing a noise model based onthe sensor and background noise analysis. The operational stage caninclude utilizing the QEF developed in the off-line design phase tocomputationally enhanced signals and data acquired and thepre-characterized platform in samples other than the reference samplesused for a QEF development. The system can include a QRI engine, whichcan further include a preconditioner to transform the incoming data to aspectral representation and to further transform the spectrallyconverted data to be compatible with a predetermined dynamical system.The QRI engine can further include an interferometric coupler to combineall the preconditioned output data with a predetermined expresserfunction, a resonance detector to detect one or more events of interestwithin the control the output data, and a quantitator to associate ameasurement magnitude with each detected event of interest.

FIG. 2 depicts a schematic of a flow diagram illustrating a process bywhich an injection of a measurement probe can cause a quantum mechanicalsystem to collapse. The received incoming unknown data can be used toinitialize a dynamical system corresponding to a modality of theincoming data at 205. The initialized dynamical system can be used togenerate a measurement probe which can then be injected into a quantummechanical system, e.g., the QEF at 210. Subsequently, it can bedetermined whether the injection of the measurement probe derived fromthe unknown input data into the quantum mechanical system results in acollapse of the quantum mechanical QEF system at 215. If such a collapseis detected, a presence of signal within the incoming data can bedetermined.

FIG. 3 depicts a flow chart of a process for using QRI to determine thepresence of a signal in incoming data. The incoming data can be receivedat 300 and the dynamical system, e.g., S-B dynamical system, can beinitialized at 305, e.g., using a trajectory of the dynamical systemthat corresponds to a modality of the incoming data. Measurement probescan be generated at 310, where the generation of the measurement probes(derived from incoming data) can based, e.g., on a modification of thetrajectory of the dynamical system. The measurement probe can beinjected into the quantum mechanical system at 315. For example, themeasurement probe can be repeatedly injected for a number of iterations.A collapse of the quantum mechanical system can be detected at 320, and,based on the collapse of the quantum mechanical system, the presence ofa signal can be detected at 325. In some implementations, the magnitudeof the signal can be based on an amount of time between injection of ameasurement probe and the collapse of the quantum mechanical system, ascaptured by the number of interferometric injection iterations.

FIG. 4 depicts a schematic of a QRI engine 400 for signal analysis. Thesystem can be divided into a design phase 405 and an operational phase410. In the design phase 405, signal analysis functions 415, e.g., theQEF, generated by a function generator 420 are determined for aparticular experimental platform that is used in the operational phase410. The QEF signal analysis functions 415 are used in the operationalphase 410 by an interferometric computational system to analyze eventsof interest, e.g., physical samples, a data stream mining, and the like.The events of interest can be associated with the particular sensorplatform. In the operational phase 410, a large number of data sets canbe analyzed that are derived from the particular platform using the sameQEF. A single noise model or QEF can be used for each sensor to achievea pre-specified LOD. The QEF need not be related to the number oftargets of interest. The QEF development protocol can utilize a smallnumber of backgrounds and representative targets for training andoptimizing the QEF for a given sensor. Once a QEF has been developed, itcan be applied to detect one or more targets within the operational dataderived from the sensor. Specification of a new LOD by the user mayrequire a new QEF to be developed. For each new sensor platform, as wellas for modifications to an existing platform, a new QEF can be generatedor existing QEF's can be altered.

In the design phase 405, a function generator 420 can receive areference data 425. The reference data 425 can include platform datathat categorizes a platform in which the physical samples are analyzed.The platform data can include platform calibration data and platformarray characteristics associated with the events of interest. Thereference data can also include calibration data that are generated byknown the events of interest in the particular platform. For example,the calibration data, e.g., calibration function 425, can include datathat is acquired in the platform from a set of specially preparedphysical samples. The function generator 420 can also receiveperformance criteria 430 which can establish desired targetspecifications such as LOD, and limit of quantitation, precision,resolution, specificity, accuracy, SNR, and the like. Based on thereference data, the function generator 425 can generate the signalanalysis functions 415. The generated functions can include expresserfunctions 435 for interferometric signal analysis, such as QEFs andstochastic resonance functions. Details regarding signal analysis usingQEFs and stochastic resonance functions and their generation can befound in U.S. Pat. No. 6,142,681 (Title: Method and apparatus forinterpreting hybridized bioelectronic DNA microarray of patterns usingself-scaling convergent reverberant dynamics; Inventor: Sandeep Gulati;Date of patent: Nov. 7, 2000) and U.S. Pat. No. 6,136,541 (Title: Methodand apparatus for analyzing hybridized biochip patterns using resonanceinteractions employing quantum expresser functions; Inventor: SandeepGulati; Date of patent: Oct. 24, 2000); the entire contents of bothpatents are incorporated herein by reference. The expresser functions435 can be based on how a dynamical system responds to excitations thatare correlated with a signal to be enhanced or with a noise that istypical in the platform. The signal analysis functions 415 can alsoinclude calibration functions 425 for quantitating signals that aredetected in the acquired data.

The operational phase 410 can involve a platform array detector 440receiving a physical sampled to produce acquired data. The operationalphase 410 can also involve a pre-conditioner 442, an interferometriccoupler 444, a resonance detector 446, and a quantitator 448. Theplatform array detector 440 can acquire data from the physical sensor,such as a CCD array or laser scanner. The acquired data can be sent tothe pre-conditioner 440, which can pre-process the acquired data. Forexample, the pre-conditioner 442 can filter the acquired data andconvert the filter data into a spectral domain. Details regardingtechniques for converting the signal pattern to a spectral domain aredescribed in U.S. Pat. No. 7,006,680 (Title: System and method forcharacterizing microarray output data; Inventor: Sandeep Gulati; Date ofpatent: Feb. 28, 2006), the entire contents of which are incorporatedherein by reference. The interferometric coupler applies the QEF definedby the function generator to calculate responses of the correspondingnon-linear dynamical system to excitations defined by the driving forcespectrum. The resonance detector 446 can process convolved data toidentify particular events of interest that can appear within theconvolved data. Based on the identified events, the resonance detector444 can detect if a signal is present in the acquired data. Due to thesignal enhancement in the interferometric coupler 444, signals can bedetected in the convolved data even if noise is several magnitudes,e.g., ten to thousand times and more, larger than the signal in theacquired data.

FIG. 5 depicts a schematic of an example of a QRI engine 500. The QRIengine 500 can include a function generator 505 in the design phase toprocess reference samples 510. Further, the QRI engine 500 can include apre-conditioner 510, and an interferometric coupler 515, a dynamicalresonance detector 520, and a quantitator 525, in the operational phase,to process acquired data 530. The reference samples 510 and the acquireddata 530 can correspond to the experimental data acquired on the samepre-characterized sensor platform. The pre-characterized platform caninclude biomolecular, biomechanical, optical, ionic, optoelectronic,radio frequency, or electronic microdevice platforms. Reference samples510 can include no-signal samples, false-signal samples, and true-signalsamples. In the design phase, the function generator 505 can generateQEF and calibration functions for signal analysis based on the referencesamples. The function generator 505 can include a noise analyzer 535, adynamical model linker 540, and a response calibrator unit 545.

The noise analyzer 535 can pre-process and analyze noise in thereference samples 510. The pre-processing can include data re-samplingand application of passive filters. The over-sampling can be performedusing interpolation techniques, such as zero padding of high-frequencycomponents. Special purpose filters can be used to decreasehigh-frequency stochastic noise and to sharpen features of interest.Details regarding these special-purpose filters can be found in thepublication titled “Scattered data fitting using a constrained DelaunayTriangulation,” (R. J. Renka and A. K. Cline, IMACS Transactions onScientific Computing 91, AI, Expert Systems, and Symbolic Computation,vol. 3, North Holland, 1992), the entire contents of which areincorporated herein by reference. The noise analyzer 535 can analyzefluctuations in the reference samples 510 using a spectral (Fourier)representation, serialize the acquired data points according to apredetermined scheme and Fourier transform the serialized data togenerate a frequency spectrum of the sensor noise. The noise analyzer535 can identify typical noise, e.g., noise signature, in thepre-characterized sensor platform based on frequency spectrum inno-signal or false-signal reference samples. The noise signature can beidentified by comparing frequency spectrums of feature probes inno-signal samples, and identifying portions of the frequency spectrumthat have small fluctuations. A tolerance can be computed foridentifying the noise signature. The tolerance can specify the allowedsensor probe-to-probe fluctuations in the noise signature, and can bebased on design parameters, such as an optimal number of frequencycomponents in the noise signature, a limit arranged for signaldetection. False-signal reference samples can be used to identify noisesignatures for probes where the false signal, e.g., clutter, modifiesthe noise spectrum.

FIG. 6 depicts a flow chart of a process for generating QEF to driveactive signal analysis by the customization of Spin-Boson quantummechanical dynamical system. The reference samples can be received,e.g., by the function generator. The noise manifested in the referencesamples can be analyzed and generalized, e.g., by the functiongenerator. Target as options can be used to derive a data core for thesensor. The data core can be a portion of the acquired sensor datacorresponding to resolution of a feature of interest. For a probecorresponding to a spot in a microarray, the data core can be defined bya circular regions surrounding pixels that represent the spot in ascanned image of the microarray. The data core can define the data thatwill be used in any further analysis of the probe. The data core can bedefined based on a sensor designed layout or user input. The size of thedata core can be optimized based on the amount of information requiredfor desired resolution and detection limits for the probe, e.g., by thefunction generator. For each data core, a sequence of data points can begenerated, e.g., by the function generator, from the acquired orpreprocessed data in the core according to a preselected serializationscheme. The generated data sequence can then be transformed into aspectral domain using 1-D, 2-D or n-D FFT and characteristic features inthe analyzed noise can be identified. In this manner, features fordeveloping and/or customizing a canonical dynamical model in theanalyzed noise can be identified. For example, the function generatorcan identify features that are typical to noise in the pre-characterizedplatform but change if a signal is present. The identified noisefeatures can be used to data or customize it cannot make all dynamicalmodel. Parameters of the canonical dynamical model can be calculatedbased on the identified noise features. The canonical dynamical modelcan be used to enhance signals that are below the nice fellow. Forexample, the dynamical model can be designed such that it respondsdifferently to different excitations. In particular, certain responsescan be smaller for excitations that correspond to the identified noisefeatures and larger for excitations that correspond to signals. Thus, inthese responses, the dynamical model choice can enhance the signalsrelative to the noise level.

The dynamical model can include a nonlinear dynamical system, such as abi-stable system, and a noise reservoir coupled to the nonlinear system.The noise reservoir and the coupling to the nonlinear system can bedesigned based on the noise features identified in the referencesamples. The noise reservoir can be represented by a stochastic forcecoupled to the nonlinear system, and parameters of the stochastic forcecan be designed according to the identified noise features. Adissipative dynamical model wherein the energy is dissipated from thesystem, e.g., by stochastic forces, can be employed. The functiongenerator can match the spectral properties of the dynamical model andthe noise features identified for the noise signature. The nonlineardynamical system is coupled to a noise reservoir that includes frequencycomponents corresponding to the identified noise feature. The functiongenerator can select couplings between the noise reservoir and thenonlinear system to match the spectrum of fluctuations, e.g., noise, inthe nonlinear system with the spectrum of the identified noise features.For example, the fluctuation spectrum of the nonlinear system can becalculated or measured for different couplings, and compared to thenoise features based on the comparison, the couplings can be varieduntil a matching criterion is met.

In addition, the function generator can set some parameters of thenonlinear dynamical system using calibrated true signal samples. Toachieve a desired resolution or LOD for signal analysis, the response ofthe nonlinear dynamical system can be calculated for excitationscorresponding to different signal levels according to the calibratedsamples. The responses to the different signal levels can be compared tothe response when no signal is present to verify whether the desiredresolution or limit of detection can be met with the dynamical model. Ifnot, parameters of the dynamical model can be adjusted to reach anoptimal resolution or LOD. The function generator, thus, defines a QEFbased on the dynamical model and the noise signature of the platformthat QEF intern characterizes the response of the dynamical model to anexcitation. The response of the dynamical model and its final state canbe determined by interferometrically coupling the QEF to the excitation.

FIG. 8 illustrates amplitude versus frequency spectra in which selectedwindows of such spectra can be used to generate a noise reservoir. Inreference 1, as illustrated in FIG. 8, the Windows identify sections ofspectra that are sensitive to changes in concentration and may beutilized to determine a sensitivity of regions of spectra. Higher orderstatistical operators including by spectral and try spectral measurescan be computed to determine properties of the regions of the spectra.The regions of frequency spectra that are of interest are determined bytransforming the spectra and to spectral energies that can be associatedwith the specific events of interest are classified as signal and noise.Subsequently, it can be determined which regions of frequency spectraare most representative of noise and/or background and/or which spectralregions are most vulnerable to background interference so that they maybe eliminated from modeling. The selected spectral regions may then bevalidated using calibrated nonspecific data. The spectral regions thatare most representative of noise may be used to generate/form the noisereservoir. Energy asymmetry between spectral energy of regions deemed tobe most characteristic of signal and spectral region's mostrepresentative of noise can then be computed to initialize transitionrate equations for the bi-stable model.

Calibrated reference samples can be used to determine if energyasymmetry is adequate to produce an observable tunneling rate whenconditions of quantum stochastic resonance are met. A qualitativedifference in tunneling rate must be observed and known examples ofsignal and no signal incoming data are introduced in the system. Astatistically significant change in tunneling rate, e.g., greater thanor equal to two standard deviations over the root mean square (RMS)noise in tunneling rate when incoming data is only noise is sufficientto conclude that a qualitatively different tunneling rate is observed. Aless stringent statistical criteria may be used if the magnitude of theaverage tunneling rate is greater than one for a particular datamodality. If the energy asymmetry is inadequate to produce a qualitativechange in the observable tunneling rate between signal and noise,synthetic resampling techniques, such as Renka Cline algorithm,convolution with the wavelet kernels, and the like, can be used togenerate additional spectral harmonics in the incoming data and theabove steps can be repeated. If a qualitative change in tunneling rateis observed, then a resonance event is detected.

An example for identifying noise signatures and for selecting frequencycomponents for the noise reservoir entails transforming the incomingdata modality into a spectral routine through Fourier transforms. Thetransformed data is then analyzed to determine the periodic city ofdifferent spectral windows using different combinations of spectralharmonics. When spectral regions at identified with the different PIDcities corresponding to signal and noise examples, then these regionsare used to compute the spectral energies to determine the energyasymmetry for initializing the bi-stable system dynamics. The noisereservoir and its interaction with the dynamical system are designed toquickly absorb noise in a choir data to be analyzed.

The noise analyzer can also analyze noise in true-signal samples usingthe same techniques as for no-signal or false-signal samples. The myspectrum can be different for true-signal samples when compared to thatfor no-signal or false-signal samples. The noise spectrum of thetrue-signal samples can also depend on the strength of the signal. Suchdependencies can be analyzed using calibrated samples, and the result ofthe analysis can be used for signal quantitation. The analysis ofcalibrated samples can also be used to set design parameters such as alower or upper signal limit for which the signal detection is planned.The dynamical modeling career can compute a QEF based on the noisesignature and the design parameters. The QEF can describe a response toan excitation of a canonical nonlinear by stabile dynamical system. Thenonlinear dynamical system is coupled to a noise reservoir by adynamical coupler. The noise reservoir has a frequency spectrum that isbased on the noise signature identified by the noise analyzer. Thedynamical coupler is defined such that, if the nonlinear dynamicalsystem receives an excitation who spectrum corresponds to the noisesignature of the sensor platform, the excitation energy is quicklyabsorb and the noise reservoir through the dynamical coupler. If thespectrum of the excitation is different from that of the noise signatureof the platform, the noise reservoir can be slow to absorb theexcitation energy. The excitation may even qualitatively change thestate of the nonlinear dynamical system.

Due to the slow DK of the excitation energy, and the excitation includesa signal who spectrum is different from that of the noise signature ofthe platform, the signal can be enhanced. If the excitation alsoincludes and noise component of the sensor platform, the signal can beenhanced because the noise is quickly absorbed in the noise reservoir.The signal enhancement depends on parameters of the dynamical system.The dynamical modeling Kurt can set these parameters to optimize theenhancement or to achieve a particular limit of signal detection.

FIG. 9 depicts a schematic diagram illustrating a dynamical model forsignal analysis. Since QEF can be used to calculate the system'sresponse to excitation, it can be used to actively and hands signals.For some systems, such as a Spin-Boson model described, the expresserfunction can be explicitly calculated. As illustrated in FIG. 9, a S-Bquantum doubled system dynamical model can be used to generate expresserfunctions for signal analysis. The dynamical model can include atwo-state (bistable) system and a noise reservoir coupled to thetwo-state. The two-state system can also be subject to a driving forcethat can and use transitions between the two states of the system. Thetwo-state (bistable) system has certain characteristics that show anoise invariance. Excitations (n) that are similar to the noise from thenoise reservoir cause negligible change to a characteristic noise (N).However, if an excitation includes signal (S) within amplitude that isabout the same or larger than a small threshold (ε), the state of thesystem and a characteristic noise N substantially change. For example,the signal interferes with the noise. Stating this schematicallyaccording to the system:

n+N is similar to N, but

εS+N is not similar to N

For example, the noise in the two-state system can be characterized by atypical transition frequency (F₀) between the two states of the system.If the system receives excitations including both signal, with anamplitude (δ), and noise N, the transition frequency depends essentiallyonly upon the signal, e.g.:

F₀[δS+N]→F₀[δS]

By repeatedly exciting the system, the signal portion, δS, can beaccumulated to reach that threshold level, ε, while the noise, N, ismostly absorbed in the noise reservoir. At the new threshold level, ε, aresonance can occur and the system can change its state. In the newstate, the characteristic frequency, F₀, starts to change its value at adifferent rate for the repeated excitations. The rate change allowsdetecting the residents. After a number of excitations, if the rate hasnot changed, no signal is present, and if the rate has changed, thesignal is present. The two state system is a nonlinear dynamical systemthat has an “|UP” state and a “|DOWN)” state separated by a barrier. Thesystem can make transitions between the |UP) and |DOWN) states. Suchtransitions can depend on a barrier height between the two states andthe energy level in the two state system. This energy level can changeto energy transfer to and from the noise reservoir and due to thedriving force.

In a physical phenomenon called stochastic resonance (SR), a periodicsignal can be enhanced using a nonlinear dynamical system similar to thetwo state system. In stochastic resonance, the periodic signal can beenhanced by increasing a noise level in the system. The noise can be astochastic noise, such as Gaussian white noise. The periodic signal canbe included in the driving force at amplitude that is insufficient to inuse transitions through the barrier separating the two states. For noiselevels that are substantially smaller than the energy barrier,essentially no transitions are and used between the two states. On theother hand, for noise levels that are substantially larger than theenergy barrier, the transitions can be driven entirely by the stochasticforces of the noise, independent from the patriotic signal. In between,the transitions can have both a stochastic component in a complementthat is correlated with the periodic signal. Near a resonance level ofthe noise, the transition complement which is correlated with the signalcan become larger than the stochastic component. Thus the periodicsignal can be enhanced relative to the noise.

Instead of a fully stochastic noise, the dynamical model can use tonoise reservoir that has a design frequency spectrum. The noisereservoir can have a frequency spectrum that is designed to enhancesignals other than patriotic signals. For example, the noise reservoircan have a frequency spectrum that corresponds to noise that is typicalin a particular type of experiment. If the two state system is driven bya driving force that includes no signal but the typical experimentalnoise, the driving force just adds the same type of noise that thesystem already receives from the noise reservoir. Thus, the system hasdynamics corresponding to an increased noise level from the noisereservoir. On the other hand, if the two state system is driven by adriving force that includes both a signal and the typical noise, thesignal can be enhanced by selecting a resonance level for the noisereceived from the noise reservoir. Thus, near the resonance level in thesystem, the signal can induce dynamics that is qualitatively differentfrom the dynamics corresponding to the increased noise level. The signalcan be detected by characterizing the dynamics of the system in responseto excitations, such as driving forces.

There is a tendency of the dynamic model to preserve equilibrium oftransition right, e.g., left to right and right to left transitions,between the two minimum. With such an arrangement, incoming data istransformed to a driving patriotic force. If the incoming data is solelycomprises noise, then it cannot be stripped equilibrium. However, ifincoming data contains signal, e.g., signal associated with an event ofinterest, it will disturb equilibrium between the two transition rights.Such disturbances in equilibrium transition right are an indicator ofsignal strength as and by deed in the different periodicity structurebetween signal and noise. If it is a large magnitude signal, it willrapidly settle in many not in computer iterations. Also, large signalcan cause high or infinite tunneling rate, small signals can exhibitslow tunneling rate, or small signals can stop tunneling from occurringcompletely. In general, high noise can increase average tunneling rate.A comparison of changes in tunneling rate between injected noise andincoming data can be determined. Thereafter, using calibrated samples,differences in tunneling rate may be determined to facilitatedistinguishing signal from noise.

In some implementations, the dynamical model is a quantum model in whichthe two state system and the noise reservoir are described by half spentoperators (Pauli matrices) and quantum oscillators (Bosons),respectively. Quantum oscillators can have only discrete energy values,e.g., they can be quantized. The quantum oscillator can have excitationsthat behave as Bosons, as opposed to fermions, because multipleexcitations can be in the same quantum state, while only one fermion isallowed in one quantum state. Spin operators, in general, described aspinning quantum object. The spin operators described a spin vectorabout which the object is spinning. The spin vector has a length thatdepends on the rotation rate. While a classical object's spin vector canpoint in any direction and can't have any length, a quantum object'sspin vector can have a length that takes only discrete values. Theshortest length is a half spin on the scale of the Planck constant. Inaddition, quantum spin vectors can have only two possible directionsrelative to a coordinate axis: up or down.

Accordingly, in the dynamical system, the |UP) and |DOWN) states aredefined as quantum states. These quantum states define a phase space ofa spin operator having an x-component, σ_(x), a y-component, σ_(y), anda z-component, σ_(z). The z-component, σ_(z), can be used to representenergy differences between the |UP) and |DOWN) states, because σ_(z) hasdifferent eigenvalues for the two states, e.g., ±1, σ_(z) |UP)=|UP,σ_(z) |DOWN)=−|DOWN. The x-component, σ_(z), induces transitions betweenthe two states; σ_(x) |UP)=|DOWN), σ_(x) |DOWN)=|UP). Therefore, the twostate system can be described using the σ_(z) operator to specify anenergy difference, E₀, between the |UP) and |DOWN) states. The drivingforce,f(t), can be added to modulate the energy difference. An effectivebarrier between the two states can be represented by the σ_(x) operatorwhose coefficient, D, corresponds to a transition frequency between thetwo states. Thus, the two state system can be represented by a spinHamiltonian, H_(s), as:

H _(s)=(E ₀ +f(t))σ_(z) +Dσ _(x)

The noise reservoir can be represented by a Boson Hamiltonian (H_(B))describing noise that is generated by multiple quantum oscillators,where each oscillator has a characteristic frequency, ω, and has anenergy described by a corresponding Boson operator, b_(ω), whichdecreases the oscillator's energy, and its conjugate, b_(ω) ⁺, whichincreases the oscillator's energy as:

H _(B)=−Σ_(ω)ωβ_(ω) ⁺βω+constant

The frequency spectrum of the noise reservoir is determined by thecharacteristic frequencies of the quantum oscillators and thereservoir's interaction with the two state system. In the noisereservoir, each oscillator is coupled to the z-component, σ_(z), of thetwo state system with a corresponding coupling, K_(ω), according to aninteraction Hamiltonian, H_(I), as:

H _(I) =H _(S) +H _(B) +H _(I)

If there is no driving force, the two state system can be in anasymmetric mixed quantum state in which the |UP) state has a smallerweight than the |DOWN) state. Between the |UP) and |DOWN) states,transitions occur with some probability. These transitions have acharacteristic frequency, F₀, that depends on the parameters, E₀, and Dof the spin Hamiltonian and the couplings between the spin and BosonHamiltonians. These parameters and couplings can be selected such thatthe asymmetry of the state and the characteristic frequency, F₀, areessentially stable for a preselected range of a total energy in themodel. From a statistical point of view, the range of the total energycorresponds to a temperature range.

If the two state system receives an external excitation, such as thedriving force, the two state system changes its asymmetric state to anew quantum state. If the driving force includes a noise component thatis similar to the noise received from the noise reservoir, the drivingforce increases only the noise level and the temperature in the twostate system without substantially altering the asymmetry of the stateor the characteristic frequency, F₀. However, if the driving forceincludes a signal component that is different from the noise from thenoise reservoir, the new quantum state can be substantially differentfrom the asymmetric quantum state that corresponds to no signal. Forexample, the new quantum state may become more symmetric or thecharacteristic frequency, F₀, may change because the signal has a weakcoupling to the noise reservoir. The substantial change of the quantumstate in response to signals is referred to as quantum resonanceinterference. The coupler is an interference coupler that is ageneralized computational unit that implements the interference betweenQEF and wave-transformed raw data. The two computational entitiesactually are two mathematical systems exhibiting QSR phenomena. Theinterference engine couples these two systems together mathematicallyand evaluates the result. The wave-wave interaction implemented withinthe interference process emulates the physical energy transfer principlethat is basic to active hardware devices.

The following mathematical steps are performed by the interferometriccoupler using the preconditioned signal pattern:

-   f ⁽⁰⁾ is defined as a vector containing the preconditioned    components from an event of interest, and f ^((i))= f ^((i 1)) Q    ^((i)) where Q^((i)) represents is the QEF after I convolutions.-   Thus,

f ⁽¹⁾ = f ⁽⁰⁾ Q ⁽¹⁾

f ⁽²⁾ f ⁽¹⁾ Q ⁽²⁾ = f ⁽⁰⁾ Q ⁽²⁾ Q ⁽¹⁾

where Q ⁽⁰⁾ represents the QEF developed in the preceding step and (itsdimensionless quantity) and where Q ^((i)) represents the i-thperturbation to the QEF, induced by perturbing one of its spectralcomponents. for k=1 to n

for j=1 to 1000 (set to a large counter value)

perturb the kth component of QEF as shown below

Q^(j)(k) = [Q^(j 1)(k) + jC₁sin (w₀j + C₁)]⁺${{{where}\lbrack x\rbrack}^{+} = {{\frac{{x\mspace{14mu} {if}\mspace{14mu} x}0}{{0\mspace{14mu} {if}\mspace{14mu} x} < 0}\mspace{14mu} {and}\mspace{14mu} C_{1}} = {\frac{1}{3}\frac{2\alpha}{360}}}};$

α denotes a small constant

Let w₀=the variance computed from the values

$\frac{{\overset{\_}{f}}_{pc}}{{Max}\left( {\overset{\_}{f}}_{pc} \right)}$

where f_(pc) denotes the preconditioned spectral vector corresponding toa known event of interest present in the arrayed pattern being analyzed.As an example, f_(pc) refers to the spectral components of the positivecontrol. Global QEF iterations may be performed if monotonic divergenceis detected between the preconditioned extraction core being analyzedand the canonical negative control, then the same convolution couplingoperations are repeated for all the spectral harmonics. The global QEFiterations are provided by

Set r ⁽⁰⁾ = q ^((j+2))

For m=1 to 25 (chosen to be a small count value)

Compute

r ^(m) = r ^(m1)+(m+j)C ₁ sin(w ₀(m+j)+C ₁)+mC ₂ sin(w _(1m) +C ₂)

where w₁ captures the variance of the components of

${\frac{\overset{\_}{f_{Nc}}}{{Max}\left( {\overset{\_}{f}}_{Nc} \right)}\mspace{14mu} {and}\mspace{14mu} C_{2}} = {C_{1} + {ɛ\frac{{Parseval}\mspace{14mu} {Avg}\mspace{14mu} {from}\mspace{14mu} {{Pos}.\mspace{14mu} {Con}.\mspace{14mu} {PM}}}{{Parseval}\mspace{14mu} {Avg}\mspace{14mu} {from}\mspace{14mu} {{Neg}.\mspace{14mu} {Con}}\mspace{14mu} {PM}}}}$

The convolution iteration can be expressed as:

$R_{kj} = \frac{{\overset{\_}{f}}^{({j\; 1})}{\overset{\_}{Q}}^{j}}{f_{nc}^{({j\; 1})}{\overset{\_}{Q}}^{j}}$

Where f_(nc) refers to the spectral components of a canonical negativecontrol, or preconditioned footprint of an event of interest known to beabsent in the arrayed image. After each convolution iteration check formonotonicity of

$\frac{R_{{kj} + 2}}{R_{{kj} + 1}} > {1\mspace{14mu} {AND}\mspace{14mu} \frac{R_{{kj} + 1}}{R_{kj}}} > 1$

if yes→then exit loop to perform global QEF iterations (that means thisparticular k component is important, i.e., we are diverging from thenegative control.)

if no → then continue   end j loop end k loopwhere Parseval Avg. from Pos. CON. PM refers to the parseval number fora canonical event of interest known to be present, and Parseval Avg.from Neg. Con. PM refers to the parseval number for a canonical event ofinterest known to be absent; and ε is chosen to be small, 0.0001. Againafter each coupler iteration compute the term

$R_{m} = \frac{\left( {\overset{\_}{f}}^{j + {m\; 1}} \right)\left( {\overset{\_}{r}}^{m} \right)}{\left( \overset{\_}{f_{Nc}^{j + {m\; 1}}} \right)\left( {\overset{\_}{r}}^{m} \right)}$

Successively compute R_(m), R_(m+1), R_(m+2). After each convolutioncheck if

$\frac{R_{m + 2}}{R_{m + 1}} > {1\mspace{14mu} {AND}\mspace{14mu} \frac{R_{m + 1}}{R_{m}}} > 1$

If the conditions of the above test are met, resonance is concluded andevent of interest is called present. If the monotonicity test fails,then the preconditioned test pattern is normalized using the expressionsbelow:

if f ^((j)) f ^(j−1) > f _(pc) ^((g)) f _(Nc) ^((c)) for any component,then

${\overset{\_}{f}}^{(j)} = {{\overset{\_}{f}}^{(j)} - \frac{{\sum{\overset{\_}{f}}^{(j)}} - {\sum{\overset{\_}{f}}^{({j - 1})}}}{25}}$

The above assumes an object with 25 spectral harmonics of interest. Thedetailed equations for the coupler unit and resonance detector unit aregiven below:

${{{{{{{for}\mspace{14mu} j} = {1\mspace{14mu} {to}\mspace{14mu} N}}{\left. {\Delta \; j}\rightarrow{j + 1} \right. = \frac{\sum{\left( {f_{i} \cdot {\hat{Q}}^{j + {1 \cdot {pm}}}} \right)/{\sum\left( {{NCF}_{i}^{0 \cdot {pm}} \cdot Q^{i + 1}} \right)}}}{\sum{\left( {f_{i}^{0 \cdot {pm}} \cdot Q^{j \cdot {pm}}} \right)/{\sum\left( {{NCF}_{i}^{g \cdot {pm}} \cdot Q^{j \cdot {pm}}} \right)}}}}{{QEF}_{r + 1} = \left\{ {{QEF}_{r} + {A\left( {j,r} \right)} + {B/r}} \right\}}{{{where}\mspace{14mu} B} = {f\left( w_{1} \right)}}{W_{1} = {\sigma \frac{\sqrt{{PSD}_{{pm} \cdot {njc}}}}{\sqrt{{manPSD}_{{pm} \cdot {njc}}}}\mspace{14mu} {and}}}{A = {{\phi_{c}\left( {j + r} \right)} \cdot \left\{ {\sin \left( {{w_{0}\left( {j + r} \right)} + \phi_{c}} \right)} \right\}}}{B = {\phi_{c_{1}}{r \cdot \left\{ {\sin \left( {w,{(r) + \phi_{c^{1}}}} \right)} \right\}}}}{\phi_{c^{1}} = {\phi_{c} + {ɛ\frac{\sigma_{1}}{\sigma_{2}}\left\{ {= 0.0001} \right\}}}}{Q^{j + 1} = {{\hat{Q}}^{j}\left( {j \neq k} \right)}}{Q^{j + 1} = \left\lbrack {{{\hat{Q}}^{j}\left( {i = k} \right)} + {\left( {\phi_{c} \cdot j} \right){\sin \left( {{w_{0}j} + \phi_{c}} \right)}}} \right\rbrack}}{{{Check}\mspace{14mu} \frac{\Delta_{{j\mspace{11mu} 1},{j + 2}}^{2}}{\Delta \; j}} > 1}\mspace{11mu} \; {\frac{\left. {{\Delta \; j} + 1}\rightarrow{j + 2} \right.}{\left. {\Delta \; j}\rightarrow{j + 1} \right.} > 1}}}\frac{\left. {\Delta \; j}\rightarrow{j + 1} \right.}{\left. {\Delta \; j}\rightarrow j \right.}} > 1$$\phi_{c} = {\frac{1}{3}\frac{2\pi}{360}}$$W_{0} = {\sigma \frac{{PSD}_{{QEFpc} \cdot {pm}}}{\max \left( {PSD}_{{{QEF};{pc}}{\cdot {pm}}} \right)}}$$W_{1} = {{\sigma \frac{{PSD}_{{QEF},{{NC} \cdot {pm}}}}{\max \left( {PSD}_{{{QEF};{NC}}{\cdot {pm}}} \right)}w_{0}} \approx w_{1}}$

Resonant Marker Identification: Finally, resonance market detectorperforms the following mathematical calculations using the convolvedsignal pattern to identify the events of interest within the convolvedsignal pattern. The resonant iteration is terminated when

${{\; {{\frac{\Delta_{{j\; - 1},{j + 2}}^{2}}{\Delta \; j} > 1}{\frac{\left. {{\Delta \; j} + 1}\rightarrow{j + 2} \right.}{\left. {\Delta \; j}\rightarrow{j + 1} \right.} > 1}}}\frac{\left. {\Delta \; j}\rightarrow{j + 1} \right.}{\left. {\Delta \; j}\rightarrow j \right.}} > 1$

or when iteration counter t exceeds present “N” (e.g., 10³ iterations)(for digital approximation to analog dynamics).

FIG. 7 depicts a schematic of a differential interference protocol. QRIallows two protocols within the interference processor, such asinterference between QEF and raw data, and differential interferencebetween QEF & raw data and QEF and a pre-specified negative control asillustrated in FIG. 7. This provides significant robustness to falsealarms in high clutter situations. The interference iterations areimplemented using an iterative control plane that entails a perturbationof QEF after each interference iteration. The perturbation protocol is afunction of the desired precision in detection objective. The energy ofQEF wave packet is increased in each perturbation. The responsecalibrator 545 defines a calibration function 550 for signalquantitation. The calibration function 550 describes the relationbetween a quantity, such as a concentration of an active agent in asample, and a signal strength that is measured with active signalprocessing. Specifically, within the QRI formalism the signal strengthis measured by resonance amplitude that describes how fast the signal inthe sample is enhanced as the quantum expresser function is applied. Thecalibration function 550 is based on calibrated samples that aretrue-signal samples exposed to controlled amounts of the active agent.The calibration function 550 uses spectral registers 555. Each spectralregister 555 represents concentration range of the active agent, andspecifies a spectral feature and corresponding region in the frequencyspectrum of a sample. (The spectral register 555 is not limited to thefrequencies of the noise signature of the platform.) The frequencyregions of the spectral register 555 are selected by comparing thefrequency spectrum of the calibrated samples, and selecting the portionof the spectrum that develops the spectral feature if the concentrationis in the range corresponding to the register 555.

FIG. 8 depicts an illustration for using a driving force impulse toexcite a two-state system that has a coupling to a noise reservoir. Thenoise reservoir is designed to generate a noise in the two-state systemthrough the coupling such that the generated noise is similar to typicalnoise in the driving force impulse. When the driving force 560 impulseis applied, energy is injected into the two-state system. The injectedenergy excites the two-state system and raises its energy. As theexcitation decays, the injected energy is redistributed betweendifferent degrees of freedom of the two-state system and, due to thecoupling, the noise reservoir. After some relaxation time, the systemreaches a new state. FIG. 8 above illustrates how the energy of thetwo-state system changes if a no-signal impulse is applied to thetwo-state system. The no-signal impulse is a driving force impulse thatincludes only the typical noise. As the no-signal impulse is beingapplied, energy is injected into the two-state system. Because theno-signal impulse has only typical noise that is similar to the noisefrom the noise reservoir, most of the injected energy is absorbed in ashort relaxation time (“T₁”) in the noise reservoir through thecoupling. After the injected energy is redistributed in a new state ofthe system, the energy has been increased by a small amount (“ΔE₁”). Theenergy increase ΔE₁ corresponds to an increased noise level due to theinjected energy. If a no-signal impulse is applied in a seconditeration, the two state system may have different relaxation time T₁′and energy increase ΔE₁′ than for the first impulse due to the previouschanges in the system.

FIG. 8, further illustrates how the energy of the two-state systemchanges if a signal impulse is applied to the two-state system. Thesignal impulse is a driving force impulse that includes a signal inaddition to the typical noise. As for the no-signal impulse, energy isinjected into the two-state system as the signal impulse is applied, andthe noise reservoir absorbs the portion of the injected energy thatrepresents typical noise in a short time. For the portion of theinjected energy that represents the signal, the decay takes a longerrelaxation time (“T2”). The injected energy is redistributed in a newstate in which the energy has been increased by a larger amount (“ΔE2”)than in the case of no-signal impulse. (That is, less energy has beenabsorbed in the noise reservoir.) The energy increase ΔE2 correspondsnot only to an increased noise level but also a characteristic change inthe quantum state of the two-state system. If a signal impulse isapplied in a second iteration, the two state system may have a differentrelaxation time T2′ and energy increase ΔE2′ than for the first impulsedue to the previous changes in the system.

The signal can be detected by comparing the system's responses to thesignal impulse and the no-signal impulse. For example, the no-signalimpulse can be generated by a system similar to the noise reservoir. Thesystem's response can be characterized by a dynamical quantity (“Θ(k)”)that is defined for a k-th iteration by a difference between the energyincrease ΔE1(k) at the k-th application of a no-signal impulse and theenergy increase ΔE2(k) at the k-th application of a signal impulse as

Θ(k)=ΔE ₂(k)−ΔE₁(k).

Alternatively, the system's response can be characterized by therelaxation time T or any other dynamical quantity that is different if asignal is present. In the operational phase, the acquired data areprocessed by the Preconditioner. The Preconditioner performs the samepreprocessing steps as the noise analyzer. The Preconditioner includes adriving force spectrum generator that generates a frequency spectrum fora force that drives the dynamical system defined by the dynamical modellinker. The preprocessed data is Fourier transformed to define a Fourierspectrum, and the force spectrum is defined by selecting thosecomponents of the Fourier spectrum that correspond to the frequencies inthe noise signature of the pre-characterized platform. Theinterferometric coupler applies the QEF defined by the functiongenerator to calculate responses of the corresponding non-lineardynamical system to excitations defined by the driving force spectrum.The Dynamical Resonance Detector detects signals in the acquired databased on a qualitative change in a dynamical quantity. The dynamicalquantity is calculated based on the data generated by theinterferometric coupler.

FIG. 9 depicts a schematic diagram illustrating time dependence of adynamical quantity in a driven dynamical model for signal analysis. If asignal is detected by the resonance detector, the quantitator usesspectral registers and a calibration function specified by the responsecalibrator to quantitate detected signal. The quantitator determinesresonance amplitude of a detected signal, selects a functional componentaccording to the spectral registers, and uses the selected component ofthe calibration function to determine a quantitative value for theconcentration of an active agent corresponding to the detected signal.

In specific implementations, the dynamical model can include othernon-linear dynamical systems, such as quantum systems with more than twostates or multiple two-state systems coupled together. Instead ofquantum systems, the dynamical model can include classical systemsdescribing the two-state system or the noise reservoir or both. Forexample, the two-state system can include a double-well potential(“U(x)”) in which a classical particle is moving along a direction x. Inaddition to a force dU/dx from the potential, the classical particle issubject the driving force f(t) and a stochastic force (“N(t)”)describing an interaction between the particle and the noise reservoir.The dynamics of the particle is described as

dx/dt=dU/dx+f(t)+N(t).

Similar to the quantum case, a response of the classical system can bedifferent for different excitations in the driving force f. If thedriving force includes noise that is similar to the stochastic noise N,only the noise level is increased in the system. If the driving forceincludes a signal, the signal may be enhanced by stochastic resonance.

FIG. 9 further illustrates how a dynamical quantity (“Θ”) changes whenexcitations are applied to a non-linear dynamical system coupled to anoise bath that is designed according to a typical noise in theexcitations. For example, the dynamical quantity can be based oncomparing the energy increase in a two-state quantum system in responseto no-signal impulses and sample impulses that may or may not include asignal, as discussed above with reference to FIG. 11. The excitations,such as driving forces, can be applied continuously or iteratively inimpulses. The presence of the signal can be detected by analyzing thefunctional form of the dynamical quantity Q as a function of the numberof iterations (or time for continuously applied driving forces). If nosignal is present in the iteratively applied sample impulses, thetwo-state system responds substantially the same way to the sampleimpulse than the no-signal impulse even as the number of iterations isincreasing. Accordingly, the dynamical quantity Q is represented by flatcurve as a function of iterations/time.

If a small signal is present in the iteratively applied sample impulses,the two-state system responds slightly different to the sample impulsethan the no-signal impulse. However, the quantum state of the two-statesystem is also changed due to the presence of the signal. The change ofthe quantum states couples back to the response of the system, whichbecomes more and more different from the no-signal case as the number ofiterations is increasing. Due to the feedback mechanism, the dynamicalquantity Q departs in a non-linear way from the flat curve of theno-signal case at a critical number of iterations. As the signal's levelis increasing relative to the noise in the sample impulses, the criticalnumber of iterations is decreasing. Further details regarding detectingevents of interest using QRI can be found in US Patent Publication No.2006/0053005 (Title: Detecting events of interest using quantumresonance interferometry; Inventor: Sandeep Gulati; Date of filing: Sep.2, 2005), the entire contents of which are incorporated herein byreference.

FIG. 10 depicts a schematic of a system 1000 for using QRI to determineif a signal is related to an event of interest or to clutter. In someimplementations, the system 1000 can include an expresser function 1004,e.g., a quantum expresser function (QEF). The system 1000 can receive afirst signal 1002 and couple the first signal 1002 with the expresserfunction 1004 using an interferometric coupler 1006, as describedpreviously. The first signal 1002 can be a reference signal. Forexample, if the object of interest is a human, then a signal from thehuman can be previously collected and used as the first signal. Theoutput of the interferometric coupling of the expresser function 1004and the first signal 1002 can be a first tunneling rate 1008corresponding to the first signal 1002. Similarly, a second signal 1010can be coupled with an expresser function 1012, e.g., a quantumexpresser function, using an interferometric coupler 1014, as discussedpreviously. The second signal can be the collected signal, wherein thecollected signal can include a signal only from the object of interest,a signal from an object that is not the object of interest, or a signalrepresenting a combination of signals from the object of interest andanother object. For example, the object of interest can be a human and areference signal from the human can be previously collected and stored.The unknown signal can represent signal from a human, signal from anundesirable object, e.g., a tree, or a signal from a human standing nextto the tree. In this example, the tree represents the clutter which canbe identified. The output of the interferometric coupler 1014 can be thesecond tunneling rate 1016 corresponding to the second signal 1010. Thefirst tunneling rate 1008 corresponding to the first signal 1002 and thesecond tunneling rate 1016 corresponding to the second signal 1010 canbe coupled with an expresser function 1018 using an interferometriccoupler 1020. For example, the first tunneling rate 1008 can beinterferometrically coupled with the expresser function 1018 and thesecond tunneling rate 1016 can be interferometrically coupled with theexpresser function 1018. In some implementations, the first tunnelingrate 1008 and the second tunneling rate 1016 can be pre-conditionedusing pre-conditioner 1024 and pre-conditioner 1026, respectively, priorto interferometric coupling using the interferometric coupler 1020. Theoutput from the interferometric coupler 1020 can be the third tunnelingrate 1022. The third tunneling rate can be input to a comparator 1024 towhich a threshold 1026 can also be input. If the third tunneling rate1022 is greater than the preset threshold, then the second signal 1010can match the first signal 1002, i.e., the unknown signal can match thereference signal. If the third tunneling rate 1022 is less than or equalto the preset threshold, the second signal 1010 can be determined to bedifferent from the first signal 1002, i.e., the unknown signal can bedifferent from the reference signal, and can, therefore, be determinedto not be a signal of interest.

FIG. 11 is a flow chart of an example of a process for identifyingwhether a signal is a signal of interest or clutter using QRI. In someimplementations, a first signal can be received at 1105. The firstsignal can be a reference signal and can be obtained from a knownsource, where the known source is the source of interest. In addition,the first signal can be buried in noise. The first signal can beinterferometrically coupled with an expresser function, e.g., a QEF, at1110, as described previously. The interferometric coupling of the firstsignal with an expresser function can produce a first tunneling ratewhich can be obtained at 1115. A second signal can be received at 1120,where the second signal can be obtained from an unknown source. Forexample, the second signal can relate only to clutter, can relate onlyto a signal of interest, or can be a combination of a signal of interestand clutter. The second signal can be interferometrically coupled withan expresser function at 1125. The interferometric coupling of thesecond signal and the expresser function can produce a second tunnelingrate that can be obtained at 1130. The first tunneling rate and thesecond tunneling rate can, each, be coupled with an expresser functionat 1135 to obtain a third tunneling rate at 1140. The third tunnelingrate can be compared with a preset threshold at 1145. If the thirdtunneling rate is greater than the preset threshold, then the secondsignal can be determined to correspond to the first signal. Inimplementations where the first signal is a reference signal, the secondsignal can be determined to be a signal of interest at 1150. If thethird tunneling rate is less than or equal to the preset threshold, thenthe second signal can be determined to not correspond to the firstsignal and can be determined to be clutter at 1155. In someimplementations, the first tunneling rate and the second tunneling ratecan be pre-conditioned prior to interferometric coupling with anexpresser function. Further, the preset threshold can be chosen suchthat a third tunneling rate greater than the preset threshold indicatesclutter while that less than the preset threshold indicates signal.

QRI can operate in a continuous operational mode over a time window ofinterest, e.g., Δ(1, 2, . . . , T) clock cycles. At the tunneling rateat an instant “i” can be scalar. Therefore, tunneling rate over time candenote a vector. Therefore, tunneling rate, TR_(Δ) is a function of timeand tunneling rate can be treated as a data vector. Using Fast FourierTransform (FFT), TR_(Δ) can be transformed into a spectral vector. Thetunneling rate spectral vector can be pre-conditioned by methodsdescribed in U.S. Pat. No. 7,006,680. The pre-conditioning process canbe applied on TR_(Δ1) to obtain a pre-conditioned input vectorcorresponding to the first signal, e.g., a reference and wellcharacterized positive signal) and on TR_(Δ2) to obtain apre-conditioned input vector corresponding to a second signal, e.g., anunknown signal which may have specific signal or may be only noise ormay represent clutter, such as non-specific signal, that can also bedenoted as a false positive which looks like signal.

If both the first tunneling rate and the second tunneling rate obtainedfrom the first signal, e.g., reference signal, and the second signal,e.g., unknown signal, respectively, have signal presence, then resonancewill be detected upon interferometric coupling. Alternatively, or inaddition, the tunneling rate vectors will be indicative of signalpresence above background. Subsequently, the two tunneling rates can beprocessed to determine if the second tunneling rate obtained from thesecond signal relates to a real signal or a false positive. QRI seeks aresonance between a properly designed QEF and any unknownpre-conditioned input from a dynamical model. Thus, QRI can be used toseek a differential coupling between signal and clutter to identifysignal from a false positive. In order to achieve this identification,QRI can be employed for interferometric coupling between a calibratedknown signal and unknown signal/clutter input.

In some implementations, the same interferometric coupler used to couplethe first signal and the expresser function, and the second signal andthe expresser function can be used to couple the first tunneling rateand the second tunneling rate, where the first tunneling rate and thesecond tunneling rate are pre-conditioned. Thus, the pre-conditionedfirst tunneling rate, which can represent the tunneling rate from thereference signal, and the pre-conditioned second tunneling rate, whichcan represent the tunneling rate from the unknown signal, can, each, beinterferometrically coupled with an expresser function, e.g., a QEF. Thedetection of resonance between the pre-conditioned tunneling rates andthe QEF can be an indication of the presence of signal. Resonancedetection can be based on turning the tunneling rate into an energyscalar and tracking monotonicity of the scalar. The duration of QRI,which can be determined by the number of QRI iterations, can be used toconclude the presence of signal. Thus, the QEF couples with thetunneling rate to conclude the robustness and persistence of signal.

Each QRI iteration can couple the QEF with the incoming signal andsimulated quantum-mechanical noise. Thus, the injectedquantum-mechanical noise can create spectral harmonics that can bedifferent in signal and clutter. This can be used as the basis fordetecting signal as a departure from noise using QRI. In the coupler,the first tunneling rate obtained from the first signal, e.g., thereference signal can be combined with a simulated quantum-mechanicalnoise and coupled with an expresser function, e.g., QEF. The secondtunneling rate obtained from the second signal, e.g., the unknownsignal, can be combined with simulated quantum-mechanical noise, andcoupled with an expresser function, e.g., QEF. The additive simulatedquantum-mechanical system can create a new spectral harmonics in thefirst tunneling rate, denoted, e.g., by New-TR1, and a new spectralharmonics in the second tunneling rate, denoted, e.g., by New-TR2. Thesenew harmonics in New-TR1 and New-TR2 can cause a change in the couplingbetween the QEF and New-TR1 that can be denoted, e.g., by TR₃₁ and TR₃₂,respectively. If TR₃₁ and TR₃₂ were both resulting from specific signal,then TR₃₁ and TR₃₂ would have the same properties and statistics, e.g.,mean, variance, and the like. The third tunneling rate can be adifference in TR₃₁ and TR₃₂ and can be a function of time. Further, thethird tunneling rate can be converted to a scalar, e.g., by averagingover some integer iteration window. The behavior of the third tunnelingrate over time can be used to infer the presence of specific signal orclutter.

In some implementations, the third tunneling rate can be comparedagainst a preset design threshold that can correspond to a conditionwhere the first tunneling rate and the second tunneling rate are bothdriven by the same reference calibration signal. So, the only differencebetween the first tunneling rate and the second tunneling rate can bethe input quantum-mechanical noise. The expresser function, e.g., QEF,can be designed such that the quantum-mechanical noise can be less thanthe measurement precision of the system. For example, the thirdtunneling rate can be concluded to be greater than the threshold if thethird tunneling rate is above the baseline, resulting from the first andsecond tunneling rate interferometric coupling, by at least 3 standarddeviations. In this manner, if the third tunneling rate is greater thanthreshold, it can be concluded that the second signal, e.g., the unknownsignal relates to specific signal.

A number of implementations of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention. Forexample, the expresser function with which the first signal and thesecond signal are interferometrically coupled can be the same expresserfunction or different expresser functions. Similarly, the expresserfunction with which the first and second tunneling rate areinterferometrically coupled can be the same expresser function as thatinterferometrically coupled with the first signal or the second signalor both. Interferometric coupling of the first signal with an expresserfunction and the second signal with an expresser function can beperformed serially or in parallel. Accordingly, other embodiments arewithin the scope of the following claims.

1. A computer-implemented method for signal analysis comprising:receiving a first signal; receiving a second signal; coupling the firstsignal with a first function generated from a first quantum mechanicalsystem to generate a first tunneling rate; coupling the second signalwith a second function generated from a second quantum mechanical systemto generate a second tunneling rate; coupling the first tunneling ratewith a third function generated from a third quantum mechanical system;coupling the second tunneling rate with the third function; obtaining athird tunneling rate; and upon determining that the third tunneling rateis greater than a threshold, identifying that the second signalcorresponds to the first signal.
 2. The method of claim 1 wherein thefirst signal is a reference signal and the second signal is an unknownsignal.
 3. The method of claim 1 wherein the second signal issubstantially similar to the first signal if the second signalcorresponds to the first signal.
 4. The method of claim 1 whereincoupling the first signal with a first function comprises: initializinga first dynamical system corresponding to a first modality of the firstsignal; generating a first measurement probe based on the initializedfirst dynamical system; injecting the first measurement probe into thefirst quantum mechanical system; and determining whether the injectionof the first measurement probe into the first quantum mechanical systemresults in a collapse of the first quantum mechanical system.
 5. Themethod of claim 4 wherein a collapse of the first quantum mechanicalsystem indicates resonance between the first measurement probe and thefirst quantum mechanical system.
 6. The method of claim 1 wherein thefirst tunneling rate and the second tunneling rate are pre-conditionedprior to coupling with the third function.
 7. The method of claim 6wherein pre-conditioning the first tunneling rate and second tunnelingrate comprises converting the first tunneling rate and the secondtunneling rate into respective spectral domains.
 8. Acomputer-implemented method for signal analysis comprising: receiving anunknown signal; coupling the unknown signal with a function generatedfrom a quantum mechanical system to generate a tunneling rate associatedwith the unknown signal; pre-conditioning the tunneling rate; couplingthe pre-conditioned tunneling rate with a reference tunneling rateobtained from a reference signal to generate an output tunneling rate;and upon determining that the output tunneling rate is greater than athreshold, determining that the unknown signal corresponds to thereference signal.
 9. The method of claim 8 wherein the unknown signalincludes one of the reference signal, noise, or a non-specific signal.10. The method of claim 8 wherein coupling the unknown signal with thefunction comprises: initializing a dynamical system corresponding to amodality of the unknown signal; generating a measurement probe based onthe initialized dynamical system; injecting the measurement probe intothe quantum mechanical system; and determining whether the injection ofthe measurement probe into the quantum mechanical system results in acollapse of the quantum mechanical system.
 11. The method of claim 10wherein a collapse of the quantum mechanical system indicates resonancebetween the measurement probe and the quantum mechanical system.
 12. Themethod of claim 8 further comprising pre-conditioning the tunneling rateby applying a Fast Fourier Transform.
 13. The method of claim 8 whereinthe reference tunneling rate is pre-conditioned prior to coupling withthe pre-conditioned tunneling rate.
 14. The method of claim 8 whereinthe reference signal is obtained from a known source.
 15. The method ofclaim 8 wherein determining that the unknown signal corresponds to thereference signal comprises determining that the unknown signal issubstantially similar to the reference signal.
 16. A system for signalanalysis comprising: a function generator to generate a first function,a second function, and a third function from one or more quantummechanical systems; a first interferometric coupler to couple a firstsignal with the first function to generate a first tunneling rate; asecond interferometric coupler to couple a second signal with the secondfunction to generate a second tunneling rate; a first pre-conditioner topre-condition the first tunneling rate; a second pre-conditioner topre-condition the second tunneling rate; a third interferometric couplerto couple the pre-conditioned first tunneling rate with the thirdfunction and to couple the pre-conditioned second tunneling rate withthe third function, the third interferometric coupler configured togenerate a third tunneling rate; and a comparator to compare the thirdtunneling rate with a threshold to determine if the third tunneling rateis greater than, or less than or equal to the threshold.
 17. The systemof claim 16 wherein the first signal is a reference signal and thesecond signal is an unknown signal.
 18. The method of claim 16 whereinthe second signal is substantially similar to the first signal if thethird tunneling rate is greater than the threshold.
 19. The system ofclaim 16 wherein the first interferometric coupler is configured toperform operations comprising: initializing a first dynamical systemcorresponding to a first modality of the first signal; generating afirst measurement probe based on the initialized first dynamical system;injecting the first measurement probe into the first quantum mechanicalsystem; and determining whether the injection of the first measurementprobe into the first quantum mechanical system results in a collapse ofthe first quantum mechanical system.
 20. The system of claim 19 whereina collapse of the first quantum mechanical system indicates resonancebetween the first measurement probe and the first quantum mechanicalsystem.